Question

A shopkeeper buys an article at a discount of 20% on the listed price from a wholesaler. The shopkeeper marks up the price by 10% on the listed price. A buyer pays Rs 231 to get it after paying a sales tax of 5% on the price asked for. find the frofit percentage.

Answer 1

$let \: listed \: price \: be \: x \: than \: cp = x - \frac{20x}{100} = \frac{4x}{5} \\ mp = x + \frac{10x}{100} = \frac{11x}{10} \\ sp = \frac{11x}{10} + \frac{5 \times 11x}{100} \\ 231 = \frac{22x + 11x}{20} = \frac{33x}{20} \\ x = \frac{231 \times 20}{33} = 140 \\ profit = mp - cp = \frac{11x}{10} - \frac{4x}{5} = \frac{11x - 8x}{10} = \frac{3x}{10} = \frac{3 \times 140}{10} = 42 \\ p\% = \frac{p}{cp} \times 100 = \frac{42}{112} \times 100 = \frac{6 \times 100}{16} = 3 \times 12.5 = 37.5\%$

Answer 2

Answer: Profit percentage would be 10%.

Step-by-step explanation:

Rate of discount = 20%

Mark up the list price = 10%

Rate of sales tax = 5%

Amount he pays to get it = Rs. 231

According to question, let the cost price be 'x'.

So, it becomes,

$\dfrac{100-20}{100}\times \dfrac{100+10}{100}\times \dfrac{100+5}{100}\times x=231\\\\\dfrac{80}{100}\times \dfrac{110}{100}\times \dfrac{105}{100}x=231\\\\x=\dfrac{231\times 100\times 100\times 100}{80\times 110\times 105}=Rs.\ 250$

After mark up, marked price would be

$\dfrac{100+10}{100}\times 250\\\\=\dfrac{110}{100}\times 250\\\\=Rs.\ 275$

So, profit % would be

$\dfrac{275-250}{250}\times 100\\\\=\dfrac{25}{250}\times 100\\\\=10\%$

Hence, profit percentage would be 10%.